Question

Is there a relationship between the dollars spent each week on recreation and the number of members of the family? Do larger families spend more on recreation? Ten Chicago families shared the following information:

Family Size 3 6 5 6 6 3 4 4 5 3

Amount Spent 99 104 151 129 142 111 74 91 119 91

a. What is the dependent variable (Y) in this situation?

b. What is the independent variable (X) in this situation?

c. Calculate ∑X, ∑Y, ∑XY, ∑X^{2}, and
∑Y^{2}.

d. Calculate SS_{XX}, SS_{YY}, and
SS_{XY.}

e. Calculate the estimated slope coefficient, b_{1}.

f. Calculate the estimated y-intercept, b_{0}.

g. Interpret the estimated slope coefficient.

h. Predict the recreational spending for a family of size 5.

i. If there are families of that size in the data set, what are the residuals for those observations?

j. Test the explanatory power of the model at a 5% level of significance.

k. Test if there is a positive relationship between family size and recreational spending. Use alpha = 0.01.

l. What is the excel command used to produce the p-value associated with the test in part k?

Answer #1

n office supply company services copiers and tracks how many
machines are serviced and the length of time (in minutes) for a
service call. The data below for 11 clients is below. Sum X = 46
Sum Y= 234 Sum XY = 5797 Sum X2 =1180 Sum Y2 =146608 1) Calculate
SSYY, SSXX, SSXY 2) Calculate b0, b1 3) Interpret the estimated
slope coefficient.

Assignment Problem: Matt Profitt, an MBA student, is studying
companies that are going public for the first time. He is curious
about whether or not there is a significant relationship between
the size of the offering (in millions of dollars) and the price per
share. Size 108 4.4 3.5 8.6 139 228 47.5 5.5 175 12 51 66 Price 12
4 5 6 13 19 8.5 5 15 6 12 12 a. Develop the appropriate scatterplot
for the two variables...

We wish to look at the relationship between y and x. Summary
measures are given below: n=5, xbar=9.4, ybar=17.2, SSxx=137.2,
SSyy=242.8, and SSxy=-169.4 Find the t test statistic for the
hypothesis H0: β1=0 vs Ha: β1≠0.

For questions #5-12, refer to the following: Data from a random
number of selected students was obtained to see if there is a
linear relationship between the hours of study (x) and the grade
(y) received on an test.
hours (x): 12 6 20 12 5 8 10
grade (y): 76 55 98 94 36 70
84
What is the value for SSxy?
What is the value for SSyy?
What is the value for SSxx?
What is the value for...

The table below gives the number of hours spent unsupervised
each day as well as the overall grade averages for seven randomly
selected middle school students. Using this data, consider the
equation of the regression line, yˆ=b0+b1x, for predicting the
overall grade average for a middle school student based on the
number of hours spent unsupervised each day. Keep in mind, the
correlation coefficient may or may not be statistically significant
for the data given. Remember, in practice, it would...

The table below gives the number of hours spent unsupervised
each day as well as the overall grade averages for seven randomly
selected middle school students. Using this data, consider the
equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting
the overall grade average for a middle school student based on the
number of hours spent unsupervised each day. Keep in mind, the
correlation coefficient may or may not be statistically significant
for the data given. Remember, in practice, it would...

The table below gives the number of hours spent unsupervised
each day as well as the overall grade averages for seven randomly
selected middle school students. Using this data, consider the
equation of the regression line, yˆ=b0+b1x, for predicting the
overall grade average for a middle school student based on the
number of hours spent unsupervised each day. Keep in mind, the
correlation coefficient may or may not be statistically significant
for the data given. Remember, in practice, it would...

The table below gives the number of hours spent unsupervised
each day as well as the overall grade averages for seven randomly
selected middle school students. Using this data, consider the
equation of the regression line, yˆ=b0+b1x for predicting the
overall grade average for a middle school student based on the
number of hours spent unsupervised each day. Keep in mind, the
correlation coefficient may or may not be statistically significant
for the data given. Remember, in practice, it would...

The table below gives the number of hours spent unsupervised
each day as well as the overall grade averages for seven randomly
selected middle school students. Using this data, consider the
equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting
the overall grade average for a middle school student based on the
number of hours spent unsupervised each day. Keep in mind, the
correlation coefficient may or may not be statistically significant
for the data given. Remember, in practice, it would...

A researcher measures the relationship between sleep medication
use (times used per week) and time spent working (in hours per
week). Are they significantly correlated? Conduct a hypothesis test
at the .05 significance level.
Sleep Medication Use
Time Spent Working
Deviation Scores
Sum of Squares
X
Y
X-Mx
Y-MY
(X-Mx)
(Y-MY)
(X-Mx)2
(Y-MY)2
8
18
3
40
6
20
2
32
Mx=
MY =
SSXY=
SSX=
SSY=
Hypotheses:
Critical Value:
r =
Decision:

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